\section{Collaborative Filtering}
Collaborative filtering systems are used to predict pr recommend items to a user. Item can be anything that make sense to give a rating, like books, movies or music. Collaborative filtering systems can have three different forms.

The first is \textbf{scalar ratings} where ratings are either numerical ratings (1-5) or ordinal ratings (good, ok ,bad).

The second is \textbf{Binary ratings} (good , bad) (true, false).

The third is \textbf{Unary ratings} is where a user has either look an item, bought an item, or just given the item a positive rating. If there is no rating it mean that there is no information relating the user to the item together (the user might have bought the item somewhere different).

ratings can be gathered by explicit means, implicit means, or even both. \textbf{Explicit ratings} is where the user is asked to give an opinion on an item. \textbf{Implicit ratings} is there it look at what actions a user is doing. An example can be. That a user that visit a page for a product might be have some interest in the product. While a user who bought the item after visiting the product are likely having a stronger interest in the product.